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  "slug": "algorithmic-graph-search-design-of-heralded-linear-optical-circuits-for-multipar",
  "title": "Algorithmic Graph-Search Design of Heralded Linear Optical Circuits for Multipartite Entanglement: A Reconciled Quantitative Assessment",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Heralded multipartite photonic entanglement underpins quantum communication, distributed sensing, and fault-tolerant computation, yet the manual synthesis of linear-optical circuits that generate a prescribed target state remains a combinatorial bottleneck. A recent preprint [1,2] recasts this design task as an algorithmic graph-search problem in the linear quantum graph (LQG) picture, reporting automated discovery of heralded circuits for hypergraph magic states, quantum error-correcting code states, general three-qubit states, and length-1 caterpillar graph states. This paper provides a single reconciled synthesis and quantitative appraisal. We formalize the search-space reduction claimed by the LQG representation with explicit combinatorial counts: for a representative six-mode, three-beam-splitter budget, raw circuit enumeration (3,375 ordered-slot instances) reduces to 455 graph instances, a factor of ≈7.4 (up to ≈44.5 under a reordering-inclusive convention), growing to ≈151 at ten modes and five beam splitters. [...]",
  "abstract_markdown": "Heralded multipartite photonic entanglement underpins quantum communication, distributed sensing, and fault-tolerant computation, yet the manual synthesis of linear-optical circuits that generate a prescribed target state remains a combinatorial bottleneck. A recent preprint [1,2] recasts this design task as an algorithmic graph-search problem in the linear quantum graph (LQG) picture, reporting automated discovery of heralded circuits for hypergraph magic states, quantum error-correcting code states, general three-qubit states, and length-1 caterpillar graph states. This paper provides a single reconciled synthesis and quantitative appraisal. We formalize the search-space reduction claimed by the LQG representation with explicit combinatorial counts: for a representative six-mode, three-beam-splitter budget, raw circuit enumeration (3,375 ordered-slot instances) reduces to 455 graph instances, a factor of ≈7.4 (up to ≈44.5 under a reordering-inclusive convention), growing to ≈151 at ten modes and five beam splitters. [...]",
  "date": "2026-10-03",
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    "titles": [
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        "title": "Algorithmic Graph-Search Design of Heralded Linear Optical Circuits for Multipartite Entanglement: A Reconciled Quantitative Assessment"
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        "description": "Heralded multipartite photonic entanglement underpins quantum communication, distributed sensing, and fault-tolerant computation, yet the manual synthesis of linear-optical circuits that generate a prescribed target state remains a combinatorial bottleneck. A recent preprint [1,2] recasts this design task as an algorithmic graph-search problem in the linear quantum graph (LQG) picture, reporting automated discovery of heralded circuits for hypergraph magic states, quantum error-correcting code states, general three-qubit states, and length-1 caterpillar graph states. This paper provides a single reconciled synthesis and quantitative appraisal. We formalize the search-space reduction claimed by the LQG representation with explicit combinatorial counts: for a representative six-mode, three-beam-splitter budget, raw circuit enumeration (3,375 ordered-slot instances) reduces to 455 graph instances, a factor of ≈7.4 (up to ≈44.5 under a reordering-inclusive convention), growing to ≈151 at ten modes and five beam splitters. [...]",
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